# Calculating moment of inertia of a complicated system

• iancheung228
In summary: The error between your calculated value for the moment of inertia of the magnets and the actual value.

## Homework Statement

I am currently doing a lab investigating the relationship between the moment of inertia and speed.
I have attached some pictures of my 'wheel' that is going to be rolled down a ramp. FYI i will be using a photogate to measure the time it takes the black strip to pass through. Initially, I thought the magnets were creating the 'hollow' part of the disc, but apparently i am wrong, and I am wondering how to calculate the moment of inertia of the magnet and then apply the moment of inertia to the equation mgh=1/2mv^2+I system (omega)^2.

## Homework Equations

MgH=v^2(m/2+Isystem/2r^2)
where M is the mass of the whole wheel system 0.369kg.
g is 9.8
H is the initial height on the ramp which is 0.105m
V is measured with a photogate ,0.10m/0.11746s= 0.85135m/s
radius of the circle is 8cm.
I of the system is (mr^2/2)+(mr^2/2)+8(mass of magnets (0.019kg(0.53m^2+2(0.078m^2))
where the mass of bgi wheel is 0.142kg and small wheel 0.074kg.

MgH=v^2(m/2+Isystem/2r^2)
where M is the mass of the whole wheel system 0.369kg.
g is 9.8
H is the initial height on the ramp which is 0.105m
V is measured with a photogate ,0.10m/0.11746s= 0.85135m/s
radius of the circle is 8cm.
I of the system is (mr^2/2)+(mr^2/2)+8(mass of magnets (0.019kg(0.53m^2+2(0.078m^2))
where the mass of bgi wheel is 0.142kg and small wheel 0.074kg.

## The Attempt at a Solution

iancheung228 said:
I have attached some pictures of my 'wheel' that is going to be rolled down a ramp. FYI i will be using a photogate to measure the time it takes the black strip to pass through. Initially, I thought the magnets were creating the 'hollow' part of the disc, but apparently i am wrong, and I am wondering how to calculate the moment of inertia

Can you explain what you mean by "I thought the magnets were creating the 'hollow' part of the disc" ?

The moment of inertia of a composite is the sum of the moments of inertia of the parts. So break it down into parts and look up the moment of inertia of each. You will need to apply the parallel axis theorem.

CWatters said:
Can you explain what you mean by "I thought the magnets were creating the 'hollow' part of the disc" ?

The moment of inertia of a composite is the sum of the moments of inertia of the parts. So break it down into parts and look up the moment of inertia of each. You will need to apply the parallel axis theorem.
yup i figured after having a conservation with another person on physics forum. is it true that there's increasing error as my magnet move towards the center of the wheel?

Error between what and what?

## What is moment of inertia and why is it important in calculating the behavior of a complicated system?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. In other words, it quantifies how difficult it is to change the rotational movement of an object. It is important in calculating the behavior of a complicated system because it helps us understand how the system will respond to external forces and torques.

## How do you calculate moment of inertia for a complicated system?

To calculate moment of inertia for a complicated system, we use the principle of superposition. This means that we break down the system into smaller, simpler components whose moments of inertia can be easily calculated. Then, we add up the moments of inertia of all the components to get the total moment of inertia for the system.

## What factors affect the moment of inertia of a complicated system?

The moment of inertia of a complicated system is affected by the mass and distribution of mass in the system. The farther the mass is from the axis of rotation, the larger the moment of inertia will be. Additionally, the shape and orientation of the system also play a role in determining its moment of inertia.

## Can moment of inertia be negative for a complicated system?

No, moment of inertia cannot be negative. It is always a positive value, as it represents the resistance to changes in rotational motion. If the calculated moment of inertia is negative, it indicates an error in the calculation or in the assumptions made about the system.

## How is moment of inertia used in real-world applications?

Moment of inertia is used in a variety of real-world applications, such as designing machines and structures, analyzing the motion of vehicles and aircraft, and understanding the behavior of celestial bodies. It is also a crucial factor in sports and athletics, as it affects the performance of objects in motion, such as balls and projectiles.